Measurement

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Measuring

There are two different types of observations. One is a description in words, such as the colour of a car or the smell of a flower. These observations are said to be qualitative (QUAL-i-tate-ive). The other type of observations involve measurements, eg a 70kg person or a 9cm mouse tail. These measurements involve numbers, and are said to be quantitative (QUANT-i-tate-ive).

In Science we need to accurately measure things so that during experiments we can compare, record changes and make conclusions about what we observe.

For example, we could measure how the temperature of water changes as it is heated by a Bunsen burner flame. Or we could measure the mass of an ice cube as it melts. If we were changing the amount of water given to plants to see if it affected the height they grew we would need to accurately measure the different amounts of water added to the plants and the height that they grew.

Units

All measurements need units. In Science there is only one standard unit for each measurement. For example length can be measured in millimetres, centimetres, metres, kilometres, etc. but the unit usually used is metres. Inches, feet and miles are not used in Science.

Note that measurements are made up of a number and a unit. For example, your heightmight be 167 centimetres. Centimetres are the units used. Without the units the number has no meaning. For example, a friend may tell you she has 1000 in the bank. You may think she is rich, until she says it is 1000 cents. So the unit is just as important as the number.

Measuring Common Quantities

The unit for volume is litres (L). To measure volume use a measuring cylinder.

The unit for time is seconds (s). To measure time use a stopwatch.

The unit for temperature is degrees Celcius (°C). To measure temperature use a thermometer.

The unit for mass is kilograms (kg). To measure mass use a scale or balance.

The unit for length /width is metres (m). To measure length use a ruler.

pH (the measure of how acidic or basic a solution is) has no units. To measure pH, either use a pH meter or a pH indicator and reference chart.

Reading the Scale

Some measuring instruments have digital readouts, eg digital watches. Other instruments have a scale with numbers on it and a pointer which moves along the scale. To read these instruments you must estimate the position of the pointer against the scale. Reading a scale is simple if you follow the five steps below.

When reading a scale you will often find that the pointer lies between two lines. In these cases you have to estimate the reading. For example, on the scale below the pointer is between the 0.6 and the 0.7 position, but not exactly in the middle. The reading is more than 0.65 but less than 0.7. It can be estimated as 0.67.

Activity: Measurement Circus

Activity: Choosing the Appropriate Measuring Equipment

Rounding Numbers

Rounding means changing a number or measurement to have fewer figures or digits in it. For example, a measurement of 3.12 may be rounded to the nearest whole number, to become 3. Rounding gives you numbers and measurements that are simpler and easier to use. Be careful - don't round numbers if you don't need to. Remember that 3.12 as a measurement is more accurate than 3.

In a calculation, you may have an answer of 5.2. The nearest whole number is 5. If the answer were 5.6, then the nearest whole number would be 6. An answer of 5.5 is exactly halfway between 5 and 6. The rule here is to always round up, so 5.5 is rounded up to 6.

Also, remember, only round off at the end of a calculation. For example:

3.2 + 2.4 = 5.6

Significant Figures

Data are a collection of facts, often as measurements, from which conclusions may be drawn.

Imagine you are using a plastic ruler to measure the length of a pen. A measurement that the pen is 16.624 869 cm long cannot be correct. A ruler cannot measure with this accuracy; the ruler's smallest increments are in millimetres. The decimal place digits (or numbers) 2, 4, 8, 6 and 9 cannot be read off a ruler. These extra digits are just guesses and have no meaning in the measurement.

In all measurements, only record the numbers that you can accurately measure. When measuring the length of a pen with a ruler, a measurement might be 16.6 cm. These are meaningful numbers, and are said to be significant figures. In this example, the pencil measurement 16.6 cm is given to three significant figures: 1, 6 and 6.

If you are using an electronic balance that gives a reading of 5.0 kg, the zero is significant. It tells you the mass to the nearest tenth of a kilogram. The reading of 5.0 kg is different to a reading of 5 kg, which is correct to the nearest kilogram. It is also different to 5.00 kg, which is correct to one-hundredth of a kilogram. The number of zeros in a measurement can tell us a lot about the accuracy of the measuring device. Always write a zero into a measurement if it is significant.

Activity: Rounding & Significant Figures Questions

Uncertainty

The figures in a measurement include the digits that are certain - the digits you can state are accurate without question - and one uncertain digit at the end, which has some possibility of error. For example, if you are using an analogue scale, you would measure this pencil as 10.7 cm.

In fact, the measurement is 10.7 cm plus a little bit. The divisions or increments on this ruler are not small enough to measure this little bit' accurately. We have reached the limit of reading of the ruler. The limit of reading is the smallest measurement of the divisions on a scale.

On the ruler drawn above, the limit of reading is one-tenth of a centimetre (one millimetre). The uncertainty in all measurements is half the limit of reading. In this case, the uncertainty is half of 0.1 cm, or 0.05 cm. This is shown in the diagram on the right.

The pencil's length of 10.7 plus a little bit could be estimated as 10.73 cm. Different people might disagree and say the measurement is 10.74 cm, or 10.72 cm. The last digit is uncertain, and so is only an estimate.

Using the uncertainty we have calculated for this ruler, we can say that the real measurement of the pencil's length is between 10.73 plus uncertainty of 0.05 cm and 10.73 minus uncertainty of 0.05 cm. In other words, the exact measurement lies somewhere between 10.68 and 10.78 cm. This is written as 10.73 ± 0.05 cm.

Uncertainty is an important idea in Science. It tells you how accurate a measurement is, and the limit of reading of the scale that has been used. Small uncertainties might not matter in everyday life but if you were designing parts for a fighter jet or a Formula 1 car, one-tenth of a centimetre could make a big difference.

Uncertainty in Digital Scales

Digital measuring devices also have some uncertainty. A digital voltmeter may record the voltage of a dry cell as 7 V. The limit of reading is 1 V, as this is the smallest increment on this scale that the instrument can measure. The real measurement of the voltage is between 6.5 V and 7.5 V.

That is, the real measurement could actually be 6.7 V or 7.2 V and, in both cases, the voltmeter would show this as 7 V. This is because this instrument has to round to the nearest whole number. The uncertainty here is written as 7 ± 0.5 V.

Converting Units

Often, it is useful to convert between the different units of measurement. An example is when you convert kilometres per hour (everyday units) into metres per second (SI units). A conversion factor is a number or ratio that allows a measurement to be converted between two different units. One way of doing the conversion is as follows.

Draw a box.
Write the conversion factor into the box.
Divide by the first number, then multiply by the second number.

Here is another conversion example - in preparing a pie grraph, you need to convert percentages to angles. There are 360° in a circle and this represents 100%. This conversion factor is written in the box to the right.

What is the angle on the pie graph for the percentage of nitrogen in the air, 78%? Look for the per cent box and divide by this number, which is 100. Then, multiply by the degrees number, which is 360. Expressed as a calculation, this is: 78 ÷ 100 x 360 = 281° on your pie graph.

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